Fairfax County supervisors, after a heated debate over whether the county government should consider the issue, urged the Reagan administration yesterday to pursue nuclear arms limitation talks with other nations.

In a vote that split along partisian lines, the board's five Democrats backed a motion by board Vice Chairman Martha Pennino that urged the president to "institute disarmament discussions" with nations that have nuclear capabilities.

"That's a long way from potholes," quipped board Chairman John F. Herrity, who joined the board's three other Republicans in abstaining from the vote.

"We should not be taking up international concerns at a board of supervisors meeting," agreed Republican Nancy Falck. "Next we'll be voting on whether to support Argentina or England," she said, referring to the Falkland Island conflict in the South Atlantic.

The issue of nuclear arms limitations has been taken before several local government bodies by antinuclear groups seeking to build grass-roots support for a nuclear weapons freeze. Both Loudoun and Montgomery counties earlier passed resolutions calling for a freeze on nuclear weapons production.

Pennino, a Democrat, said her concern over the "proliferation of nuclear warheads" prompted her decision to introduce the Fairfax resolution. "All of us, I am sure, feel it would be not only ridiculous but disastrous for the United States to take a unilateral position reducing its nuclear power," Pennino argued during the meeting.

"But we also realize that presently there are enough warheads to destroy this planet seven times over," she said. "Once dead is dead. You don't die seven times," she said.

While the resolution passed by the Fairfax supervisors stops short of calling for a nuclear arms freeze, representatives from a local antinuclear group said they were pleased that the board took up the issue.

"We think it is fine that the board is asking for a return to nuclear arms limitation negotiations," said Nan Rodney, a county resident who is coordinator of the Northern Virginia Coalition for a Nuclear Weapon Freeze. "But I think we will still press for a more specific resolution that calls for a freeze on nuclear arms," she added.