Mindful of Fairfax City's veto last year of a regional gasoline tax, the Northern Virginia delegation to the Virginia General Assembly adopted a cautious attitude today toward new legislation that would bypass the city's objections to such a tax.

At a caucus of the delegation, the legislators agreed to withhold introduction of the new legislation until they can receive a written promise from each of the five Northern Virginia localities that they will not oppose the new measure.

The new measure would allow each of the localities - Fairfax City, Falls Church, Alexandria, Fairfax County and Arlington County - to impose a 4 per cent sales tax on gasoline. If enacted by all localities it would raise between $10 million and $12 million annually, which would be used for local transportation needs, according to Sen. Wiley F. Mitchell (R-Alexandria).

Last year the Assembly approved a measure allowing the localities to impose such a tax to meet their soaring Metro transit system deficits. But the tax required approval of all fire jurisdictions and to the surprise of some legislators. Fairfax City refused to enact the measure.

Fairfax City government spokesman Robert Becker said today that the city does not object to provisions of the latest bill, which will leave enactment of the tax up to each locality.

Several members of the delegation have indicated they will sponsor new legislation on the measure during the current session, but they delayed introduction of the bill today until the localities agree to "put in writing," as Del. Warren G. Stambaugh (D. Arlington) put it, their position on the measure.

Today, the 100-member House of Delegates gave its first approval to any legislation of the new session, supporting a measure that will allow left turns onto one-way streets after stops at red lights.

The left-turn provision was supposed to be part of a right-turn-on-red law enacted by the Assembly last year, but was inadvertently left out of the bill, according to Del. Lewis A. McMurran Jr. (D-Newport News), sponsor of the measure.