Negotiators working on a deal to limit Iran's nuclear program agreed Friday to extend an interim agreement until Monday to give them more time to work.

"We still have a couple of very difficult issues, and we'll be sitting down to discuss those in the very near term – this evening and into tomorrow," Secretary of State John Kerry told reporters in Vienna, where the talks are being held. "But I think we have resolved some of the things that were outstanding and we've made some progress."

Negotiations hit a snag on Thursday when Kerry balked at escalating Iranian demands likely to cause political problems for any agreement in Congress and threatened to walk out. Iranian officials meanwhile accused Washington of changing its position and said they would not succumb to "psychological warfare."

The latest extension of the November 2013 interim deal is the third in just the past two weeks as negotiators from Iran and the P5+1 countries — the United States, Britain, France, Germany, Russia and China — try to close out a final agreement on the basis of a framework announced April 2.

But fleshing out the details have proved elusive, in part due to new Iranian demands on sanctions relief and limiting access to international inspectors who would verify any deal. Conceding on those demands would amount to backtracking from what was announced in the framework. Tehran has also demanded an end to the U.N. arms embargo against it, and has split the P5+1 by securing Russian backing for the move.

On Thursday, Kerry publicly threatened to walk away from the talks even as he and other negotiators said they were very close to a final agreement, saying "difficult decisions" need to be made "very soon."

"If the tough decisions don't get made, we are absolutely prepared to call an end to this process," he told reporters in Vienna.

RELATED: Iran nuclear talks hit a brick wall

In response, Iranian officials accused the United States of shifting its demands. Ali Akbar Velayati, an adviser to Ayatollah Ali Khamenei, Iran's supreme leader, said Iranian negotiators "will not succumb to any pressure or psychological warfare," according to the official Islamic Republic News Agency.

The Iranians appear to have been successful at getting the P5+1 to make further concessions in the latest round of talks, most notably on sanctions relief and verification issues. This has put the U.S. negotiating team under severe pressure from lawmakers in Congress, most notably the Democrats on whom approval of a deal rests, and it appears the latest demands have pushed the talks to a red line they cannot cross without risking that support.

President Obama, who has been meeting with lawmakers on Iran, held a conference call late Wednesday with the negotiating team ahead of Kerry's statement.