VIENNA — Secretary of State John Kerry began on Saturday what the Obama administration hopes will be the final push for a nuclear accord with Iran, just three days before a deadline for concluding an agreement.

However, American officials have almost discounted the notion that a deal will be made by Tuesday’s deadline. Their goal is to bridge a number of technical and political divides over the next week in hopes of getting a final accord to Congress by July 9.

If the administration hits that target, Congress will have 30 days to review the accord under the terms of legislation that President Obama signed in May. If a deal came later in the summer, that review period would extend to 60 days because of the August congressional recess, which would give opponents in Congress more time to mobilize against the agreement.

“I think that everybody would like to see an agreement, but we have to work through some difficult issues,” Mr. Kerry said at the start of his meeting with his Iranian counterpart, Mohammad Javad Zarif.