Montgomery and Prince George's counties are asking the Maryland General Assembly to substantially increase the state's share of Metro construction costs despite stiff resistance from Maryland transportation officials.

Although the state agreed in 1972 to spend $161 million for two counties' contributions to building the 100-mile system, the amount assessed has risen to $213 million because of increased costs of materials, labor disputes and construction delays, according to the counties.

Instead of increasing local taxes, Montgomery and Prince George's officials argue that the state should pick up the $52.1 million increase.

In a bill that has been approved by the two counties' House delegations and soon will be considered by the senators, the counties also are asking the state to extend its pledge for Metro payments through 1983.

So far, State Transportation Secretary Hermann Intemann has been unwilling to support the counties' stand.

While he will not declare himself on the specific bill, Intemann has previously stated that making decisions on future subway expenditures is premature.

"Until we see what's going to happen to the transportation bill in Washington," he said yesterday, "everyone's spinning their wheels as to new financial commitments." Intemann was referring to the uncertainty over continued federal support - now amounting to 80 per cent - on interest paid on Metro bonds.

"Rights now we're sticking to our $161 million" for the two counties, Intemann said.

Montgomery and Prince George's Counties, with the help of Baltimore, won support for the Metro funding act in 1972. That law, which expires at the end of June, states there should be parity between Maryland's rapid rail transit support for the Baltimore and Washington area subways.

The Montgomery County administration's position is that this parity has not existed and consequently the county is entitled to its requested increase from the state.

In addition, Montgomery County lobbyit Ed Sealover contended before the county House delegation yesterday that it would be "safe to assume" that the state's appropriation for the Baltimore system would rise concurrently with the increase in costs of Baltimore subway construction.

In an interview yesterday, Intemann suggested that many not be a reliable assumption. "Our share of the Baltimore subway was to be $148 million, but we may not have additional money for other costs," the transportation secretary said.

Another Potential derailment for the bicounty Metro bill is its inescapable association with the bitter controversy over the Baltimore subway within the legislature.

"There's not a hell of a lot of sympathy for the Baltimore subway," Sealover acknowledged, "and that attitude could work against Metro."

That point was underscored yesterday before a Senate Budget and Taxation Committee hearing on a proposed bill by Sen. Frederick C. Malkus (D-Dorchester) to end work on the Baltimore subway as of July 1.

Reiterating the familiar argument or rural subway opponents, Malkus said, "There is no way we can maintain our roads and keep the subway."

Intemann objected to Malkus's bill, saying that if Maryland backed out now it would have to repay all the money the federal government had kicked in to get the project going.