Secretary of State Tony Blinken warned Israeli leaders on his visit to Jerusalem this week that evictions of Palestinian families from East Jerusalem or further unrest on the Temple Mount could spark renewed “tension, conflict and war," he told me in a phone interview.

What he’s saying: Speaking on his flight back from the Middle East, Blinken said the most important aspect of his trip was that he heard directly from Israel and indirectly from Hamas, through Egypt, that both want to maintain the ceasefire. “But it's also important that we avoid various actions that could unintentionally, or not, spark another round of violence," Blinken said.

“We raised the concerns that we have on all sides with actions that in the first instance could spark tension, conflict and war and also ultimately undermine even further the difficult prospects for two states," he said.

• While meeting with Israeli officials, Blinken mentioned “evictions of Palestinians from their homes where they lived for decades and generations, the demolitions of housing as well... and of course everything that took place on and around the Temple Mount," or al-Aqsa Mosque compound, where confrontations between police and protesters continued even after the ceasefire.
• With Palestinian leaders, "we raised incitement to violence or letting violence go forward with impunity," Blinken said, as well as the "very problematic" payments made to the families of Palestinians convicted of terrorism.
• He would not characterize the responses of either side to those warnings, saying he’d let them speak for themselves about “how they're taking all that on board."

Why it matters: Israel’s Supreme Court asked the attorney general to submit by June 8 his legal opinion about the impending expulsions of Palestinian families from the Sheikh Jarrah neighborhood of Jerusalem in favor of Jewish settlers. The potential expulsions drove the protests that preceded the fighting in Gaza

• The delay gives the Israeli government the opportunity to ask the court not to order the evictions or to seek another solution to avert a new crisis.

Driving the news: Blinken's flight took off from Jordan, where he'd met with King Abdullah II. One of the main issues discussed was the situation in Jerusalem and Sheikh Jarrah in particular, the Royal Court said in a statement.

• On the flight back home, Blinken called the foreign ministers of Saudi Arabia and Qatar. He updated them on his talks in the region and asked for their support for humanitarian and development efforts in Gaza.
• Qatar announced on Wednesday it would donate $500 million for the reconstruction efforts in Gaza.

The big picture: Blinken said one takeaway from his trip in the region and the events of the last several weeks is that the conflict between Israelis and Palestinians has "not magically disappeared," and needs to be addressed.

• The Secretary of State pushed back on the suggestion that the Biden administration neglected the conflict in its first few months in office, noting its early steps to reengage with Palestinians.
• But he acknowledged that the administration didn't put much emphasis on the peace process because the conditions were not ripe for any progress, particularly due to the ongoing government formation process in Israel and the delayed Palestinian elections.
• “In the absence of more positive conditions, I think it is hard to see what utility there would be in making some kind of major push right out of the box," he said.
• That's an issue "for tomorrow," Blinken said. "There's a lot to be done to get to a place where realistically we can see prospects for doing something meaningful."

The state of play: Blinken said the most urgent matter is to build on the ceasefire in Gaza and lay the foundations for greater stability in the West Bank and Jerusalem.

• “The ceasefire was not an end in itself, as important as it was, but also a means to have some space to start to build something a little bit more positive," he added.
• The Biden administration wants to move as fast as possible on the reconstruction of Gaza. Blinken said the process has to be led by the UN together with the Palestinian Authority and Egypt and be done in a way that will assist the population but not benefit Hamas.

Yes, but: The Israeli government said it would not allow the reconstruction of Gaza without progress toward the return of the bodies of Israeli soldiers and the release of Israeli citizens held by Hamas. Israel and Egypt tightly control the borders of the Gaza Strip.

• Israel also announced new restrictions on the entry of goods into Gaza, for example blocking chocolate powder on Thursday because it wasn’t designated as humanitarian aid.
• “We fully understand the deep need to bring the remains of the soldiers and the Israeli citizens back home. And to the extent that we can help in any way we certainly will. At the same time, I think there are very urgent needs for many people in Gaza that needs to be addressed," Blinken said.

The Secretary of State said the "one of the best means" to help prevent a cycle of violence is to increase the opportunities available to people in Gaza.

• “What Hamas feeds on is the lack of hope and lack of opportunity. So the best answer is to try and provide that and to make sure that the Palestinian authority has a role to play in delivering that hope and opportunity, as well as others including Israel, so I think it makes a profound strategic sense — never mind mind the importance on a human level”.

What’s next: During his visit to Israel, Blinken announced that the Biden administration would move forward with reopening the U.S. consulate in Jerusalem that was shut down by the Trump administration.

• As Axios has reported, Israeli Prime Minister Benjamin Netanyahu told Blinken he had reservations about this move. But Blinken told me the move was both necessary and in Israel's interest.
• Blinken stressed the reopening of the consulate won't change the U.S. recognition of Jerusalem as Israel's capital, nor mean any recognition of Jerusalem as a capital for the Palestinians, which he said was a matter for direct negotiations between the parties.

“So I think there is no basis for concern. To the contrary, I think, it is beneficial to everyone. If we're not engaged with the Palestinians that undercuts our ability to advance things that I think would be everyone's benefit, including Israel," Blinken said.

Go deeper:Inside Biden's response to the Gaza crisis