King Hussein is pressing Palestinian leader Yasser Arafat in their talks here to commit himself to recognizing Israel within its pre-1967 borders, a Jordanian official said today.

Arafat implicitly recognized Israel's right to exist by endorsing the resolutions of the Arab summit at Fez, Morocco, last month. The Jordanian official, who asked to remain anonymous, suggested that Jordan wanted a more open form of recognition to send a signal to the United States that progress could be made under President Reagan's Middle East peace initiative.

Both sides appeared optimistic on the second day of Arafat's visit for comprehensive talks on the goals of Jordanian-Palestinian relations.

There were no signs, however, of how they expected to resolve the difficult question of whether to propose that the Palestinian territories currently occupied by Israel should eventually become an independent state or an entity federated with Jordan.

An informed Jordanian source said the king was pushing hard for a federation, which would be along the lines of Reagan's proposal. A Palestine Liberation Organization spokesman said the two sides were seeking to implement the resolutions of the Fez summit and the Palestine National Council charter, both of which provide for an independent state.

The PLO spokesman, Ahmed Abdul Rahman, said Jordan and the PLO expected to reach a formal accord on the issues and would establish committees to implement their decisions.

"We will work together as one party," he told reporters.

There was no public Jordanian statement on the negotiations, but media reports stressed that the first round of talks had gone positively.

In another sign of good feelings, Jordan this evening permitted the first public PLO rally since the so-called Black September battles fought in 1970 between Jordanian and PLO forces.

Arafat, whose visit here ends Wednesday or Thursday, delivered a rousing 40-minute speech to about 2,000 Palestinians jammed behind the PLO center here, saying, "In Beirut, we taught Israeli Defense Minister Ariel Sharon a lesson he will never forget."

It was impossible to judge how much pressure Hussein was exerting on Arafat to make him pledge recognition of Israel. A Western diplomat suggested that the talks here might lay the groundwork for the National Council -- the PLO parliament-in-exile -- to offer at a meeting expected within the next month to recognize Israel in exchange for creation of a Palestinian state.

The diplomat said that the Jordanians appreciate the importance of recognizing the Jewish state before any major steps can be taken toward a solution of the Palestinian issue.