Axios

President Trump praised Chinese President Xi Jinping on "The Axios Show," calling him one of the world's greatest leaders, "very smart" and "all business."

Why it matters: Trump has long admired leaders who wield centralized power and stamp their will on history. He skipped over traditional American allies when asked which world leaders he respects.

President Trump tells "The Axios Show" that his deal to end the war in Iran averted a global depression, that Cuba could get the same treatment as Venezuela, and that a leading AI lab looked in recent days like a national security threat.

The big picture: In a sweeping 45-minute interview on Thursday with Axios White House correspondent Marc Caputo, Trump made clear his view of the extent of his post-war power: "There are no limits."

President Trump declared on "The Axios Show" on Thursday that he's discovered "no limits" to his power since going to war with Iran.

• A forthcoming book reveals he's been entertaining an even grander idea: that he may be the most powerful man in history.

Why it matters: Trump is no longer merely testing the limits of the presidency. He's describing power in world-historical terms — placing himself in the lineage of conquerors, dictators and strongmen who bent nations to their will.

Two U.S. officials told Axios on Friday that Israel and Hezbollah had agreed to a renewed ceasefire in Lebanon, but clashes continued even after it was supposed to be in effect.

• Hezbollah sources told Reuters the group would observe the ceasefire, but a spokesperson for Israel's military declined to confirm its participation.

Why it matters: The continued fighting between Israel and Hezbollah led to the postponement of U.S.-Iran talks planned for Friday. U.S. officials hope the talks can be launched if the ceasefire holds.

Vice President JD Vance postponed a planned trip to Switzerland for U.S.-Iran talks expected to begin Friday, the White House said.

Why it matters: The White House said the reason for the change of plans was "logistics." But there were some indications that the background for the decision is connected to the shaky ceasefire in Lebanon.

President Trump denied that the Iran war revealed the limits of his ability to exert power, telling "The Axios Show" he still believes there are "no limits."

The big picture: Trump entered the war demanding "unconditional surrender." He ended it with a limited memorandum of understanding instead.

• Trump acknowledged to Axios' Marc Caputo that he'd negotiated that deal to keep the war from turning into a global economic depression.

The political arm of the Congressional Hispanic Caucus is quietly putting massive sums into helping the group's chair, Rep. Adriano Espaillat (D-N.Y.), win his primary, Axios has learned.

Why it matters: The spending signals how much peril Espaillat's allies think he is facing from democratic socialist challenger Darializa Avila Chevalier.

Iran's supreme leader, Mojtaba Khamenei, said Thursday he authorized direct talks with the U.S., but warned they do not signal agreement with Washington.

Why it matters: Khamenei's comments Thursday, in a written statement on his Telegram channel, were his first response to the signing of the U.S.-Iran memorandum of understanding (MOU).

Vice President Vance on Thursday issued a blunt warning to members of the Israeli government who have been attacking the deal with Iran: President Trump is the only friend you have left, and it would be unwise to cross him.

Why it matters: Vance gave public voice to the consternation many on Trump's team have felt with Prime Minister Benjamin Netanyahu's government over the past three months. He also issued a veiled threat that if Israel undermines the deal, U.S. military support could be impacted.

The U.S. national average gas price has dropped back below $4 a gallon, per AAA, a sign of Americans' pain at the pump easing after months of war in Iran.

The big picture: Iran's squeeze on oil traffic through the Strait of Hormuz battered the global economy. But crude prices in June fell to their lowest levels in over three months on news of an extended ceasefire agreement between the U.S. and Iran.