The D.C. voting rights amendment passed its first major test in the Maryland Senate today after D.C. Del. Walter E. Fauntroy reassured suburban Washington legislators that a commuter tax would not be sought in this session of Congress.

The amendment had run into unexpected trouble in the past three days after U.S. Rep. Ronald V. Dellums (D-Calif.), new chairman of the House District Committee, said he planned to ask Congress for authority to impose the tax on nonresidents who work in Washington.

Fauntroy visited legislators from Montgomery and Prince George's Counties yesterday and today, allaying their fears of a commuter tax. The amendment sailed through a Senate committee this morning by a vote of 6 to 2.

"We were in very serious trouble (after the Dellums statement)," said Sen. Clarence M. Mitchell III, sponsor of the resolution to ratify the amendment that would give the District two U.S. senators and at least one representative.

"If Fauntroy hadn't cleared the air," said Mitchell, a Baltimore Democrat, "you would have had the Washington area guys all working against us."

Mitchell said several senators from Prince George's and Montgomery counties who were committed to vote for ratification had "backed off" until Fauntroy gave them personal assurances in a series of meetings yesterday and today.

By promising to put the commuter tax question "on the back burner" at least for this year, Fauntroy appeased other legislators who were seeking a delay in the ratification vote until they could get such a "moral commitment" from District leaders. (Dellums has now acknowledged that the commuter tax is "on the back burner" and will be pushed only if Mayor Marion Barry requests it.)

Prince George's Sen. John J. Garrity, who sponsored a resolution to submit the ratification question to voters in the 1982 election, said he would now vote for the amendment. "It would have been very hard without the backoff (from the commuter tax)" he said.

The amendment is now headed for the Senate floor, where it is expected to come up for a vote Tuesday. Mitchell said he has commitments from 30 senators, six more than needed for passage.

Suburban Washington legislators had solidly supported the measure until Dellums reawakened their fears of a commuter tax this week. The chances of passing such a levy in Congress would improve, some lawmakers believe, if the District elected voting members to Congress.

In past appearances here, Fauntroy consistently refused to promise that District leaders would not push for a commuter tax, saying the issue of voting rights for District citizens is separate from the tax matter.

Realizing that Dellums' statement set back ratification efforts here, Fauntroy said today, he decided he had to give Maryland legislators the commitment they had been seeking.

The commuter tax, he said, is "not now on our priority list. We do not now plan to introduce it." That promise is only good for the current session of Congress, he added, saying, "I can't make a commitment for subsequent years."