President Reagan, in another round of election-year jockeying with Democrats over rising unemployment, plans to break with tradition and sign a job training bill at the White House today without the presence of members of Congress who steered the measure to passage.

A presidential spokesman, C. Anson Franklin, said that the White House had invited four Republicans to the ceremony, but they could not attend because of previous commitments. That "affected the decision" to sign the bill without any House and Senate members present, he added.

"We went after our Republican sponsors," said Deputy White House press secretary Larry Speakes. "It wouldn't make any sense to do it without them, or with just the Democrats."

So, instead of the bill's sponsors looking on while the president signs the legislation, White House officials were considering a plan yesterday to have unemployed workers who would benefit from training, or interest groups who favored the bill, in to witness the event.

Earlier yesterday, Reagan told reporters that House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) would be welcome at the bill-signing scheduled for noon today. "The door's always open," the president declared.

But other Democrats in Congress who worked on the job-training bill were informed by White House officials later yesterday that no members were being invited.

Several Democrats, including O'Neill, said they could have been available if they had been invited.

The job training bill has been the subject of intense controversy recently as unemployment has climbed to record post-Depression levels.

Reagan has embraced the legislation as an example of his concern over the rising joblessness. But Democrats complain Reagan is trying to grab credit for the measure just before the election and that his administration originally opposed it.

The bill must be signed by Saturday. The White House had originally invited members of Congress to a signing ceremony last week, but it was canceled when O'Neill, who also must sign the legislation, held a ceremony in his office.

Sen. Dan Quayle (R-Ind.), chief GOP Senate sponsor of the job-training bill, was in Indiana and could not break previous commitments to return to Washington today for a ceremony, an aide said. But Quayle had told White House officials he would be available any other time this week, the aide added.

Sen. Edward M. Kennedy (D-Mass.), the leading Senate Democrat sponsoring the legislation, "could have been available," an aide said, but the White House did not extend an invitation. Rep. Augustus F. Hawkins (D-Calif.), a leading House sponsor of the bill, also was told that no members of Congress were being asked to attend the ceremony, a spokesman said.

The maneuvering over today's signing ceremony came as the president prepared to deliver a speech on the economy tonight that White House officials described as a "progress report." Democrats asked the three TV networks not to provide free air time for the address on the grounds that it is blatantly partisan, just three weeks before Election Day.

As of late yesterday, CBS, NBC, and Cable News Network had agreed to carry the speech, scheduled for 7:30 p.m., while ABC refused. NBC and CBS also confirmed yesterday that they had rejected a request to sell 30 minutes of prime time to Republicans during the middle of this week, the Associated Press reported.

"We don't tell them how to run their business," Speakes said of the networks yesterday. "You don't tell us how to stage the news and we don't tell you how to cover it."

Questioned about the speech at another bill-signing yesterday, Reagan again suggested it would not be partisan. "Doesn't everyone want the economy to get better?" he asked.

Even with rising unemployment, the White House asserted yesterday that Reagan remains a valuable commodity for GOP Senate hopefuls. Speakes said that polling data showed that Reagan's visits in Montana and Nevada had been worth "five to 10 points" for Republicans. Other strategists in both parties say that while Reagan may achieve those results in Sun Belt and western states, his appearances in the recession-hit Midwest translate into much smaller gains.

The president briefly stepped away from the economy and the campaign yesterday to sign legislation that would expand the legal protections for victims and witnesses of crimes. In a Rose Garden ceremony, he also signed a bill to help parents locate missing children.

Among those who witnessed the signing were John and Reve Walsh of Hollywood, Fla., and their 3-month-old daughter, Meghan. Their 7-year-old son, Adam, was found murdered after he disappeared for two weeks in 1981. They have since set up a center to help parents locate and identify missing children.