Mr. Obama, according to two people familiar with the discussion, told Mr. Kerry and Mr. Moniz to ignore the deadline, make it clear that the president was ready to walk away and leave all sanctions on Iran in place, and see if that would change the dynamic.

It is still not clear if the last-minute change in tactics will succeed in convincing the Iranians that the Obama administration does not want the accord more than they do, or yield a different result…

Germany’s foreign minister, Frank-Walter Steinmeier, said before the meetings Wednesday night that the Iranians were expected to present “new recommendations” on how to bridge the gaps that have been holding up the accord.

“Naturally, whoever negotiates has to accept the risk of collapse,” said Mr. Steinmeier, who made it clear he was staying for another day. “But I say that in light of the convergence that we have achieved here in Switzerland, in Lausanne, it would be irresponsible to ignore the possibility of reaching an agreement.”