U.S. Appeals Court Judge Robert H. Bork met with key Senate Republicans yesterday as the GOP lawmakers said they will press the Democratic majority for quick Senate action on his nomination to the Supreme Court.

In his initial round of courtesy calls on Capitol Hill, Bork met with Senate Minority Leader Robert J. Dole (R-Kan.), Sen. Strom Thurmond (S.C.), the ranking Republican on the Senate Judiciary Committee, and Minority Whip Alan K. Simpson (R-Wyo.), a Judiciary Committee member.

Thurmond said he hopes that the committee will clear the nomination for floor action by the full Senate by mid-September, giving Bork a chance to be confirmed before the start of the Supreme Court's new term on Oct. 5.

"We want to get this thing going as soon as we can," Dole said as he, Thurmond and Simpson met with Bork in Dole's office.

Dole and Thurmond later went to the Senate floor, where they again urged that Bork, nominated to replace retired justice Lewis F. Powell Jr., be confirmed in time to begin serving when the court reconvenes.

However, one Judiciary Committee Democrat said the Republicans' proposed timetable is unrealistic. "There is no chance in the world of that happening," said Sen. Howard M. Metzenbaum (D-Ohio). He said he does not expect the committee to begin hearings on the nomination until after Labor Day.

The first skirmishing over the Bork nomination is likely to center on timing, with the White House and Senate Republicans demanding a vote on confirmation before Oct. 5 while Democrats insist that a thorough investigation will take longer than that. Some Democrats have predicted that the confirmation fight, including a likely filibuster on the Senate floor, could stretch into November and beyond. Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.) is to meet today with fellow committee Democrats to discuss timing and other aspects of the confirmation process.

Biden spent yesterday at his home in Wilmington meeting with committee aides and officials of his presidential campaign.

Meanwhile, one of Biden's rivals for the 1988 Democratic presidential nomination, Sen. Paul Simon (Ill.), predicted that Bork's nomination will be stopped by a filibuster and indicated that he will oppose the nomination. "Certainly my tilt at this point . . . is to say this man should not be on the court," he said in Iowa.

Simon, a member of the Judiciary Committee, said Bork is "mentally qualified, no question, academically qualified." But he added, "When you say close-minded, there is a serious question. I do not want someone who is a rigid ideologue, and this man appears to fit that mold."

Simon also said that "the odds are against approval" of the nomination because he thinks it is unlikely that Bork's Senate supporters will be able to muster the 60 votes needed to end a filibuster.

Meanwhile, Sen. Bob Packwood (R-Ore.) said yesterday that his attitude toward the nomination will hinge on Bork's view of Roe v. Wade, the Supreme Court's landmark 1973 decision that overturned state laws banning abortion.

Packwood, a leading Senate advocate of the "pro choice" stance on abortion, said he will ask Bork about his description of Roe v. Wade as "an unconstitutional decision, a serious and wholly unjustifiable usurpation of state legislative authority."

If Bork intends "to upset Roe v. Wade or limit it, I will oppose the nomination" and filibuster against it, Packwood said.

Bork's confirmation is vehemently opposed by pro-abortion groups, among others, because Powell provided the critical vote for the majority in the 1973 abortion decision.