RICHMOND — A proposed amendment to the state constitution creating a bipartisan commission to draw Virginia's political map advanced in the Senate on Tuesday but faces an uncertain future in the House of Delegates.

The Senate Privileges and Elections Committee voted 13-1 to approve the constitutional amendment, which will go next to the Finance and Appropriations Committee to address its cost.

The resounding, bipartisan vote signals the depth of support in the Senate for the commission, which was first approved last year when Republicans controlled the General Assembly.

Democrats who won majorities in both chambers of the legislature last fall campaigned on the need for redistricting that was free of political influence. But after they won, some in the party expressed doubts about enacting last year’s plan.

Members of the Virginia Legislative Black Caucus, in particular, have said all along that the mechanism designed by Republicans does not do enough to ensure minority representation.

For instance, if the commission is unable to come up with a viable map, the issue would go to the justices of the Virginia Supreme Court — which some Democrats complain has been stacked with conservatives after two decades of Republican dominance in the legislature.

In Virginia, proposed constitutional amendments have to pass in identical form for two consecutive years before they go on the ballot for public approval, so the current measure can’t simply be modified. The clock is ticking because redistricting will take place next year, after the 2020 Census.

Without a new system, the state would follow past practice: The state’s 140 legislative districts and 11 congressional districts would be drawn by the legislature and subject to the governor’s approval, like any other legislation.

Virginia has had trouble with that approach since the maps were last drawn in 2011 by a Republican-led House and Democratic-controlled Senate. The U.S. Supreme Court twice ordered do-overs after federal courts found the legislature had packed too many African American voters into a Hampton Roads-based congressional district and 11 House of Delegates districts.

Senate Democrats indicated Monday that they would prefer to keep the proposed amendment, which was carried by Sen. L. Louise Lucas (D-Portsmouth), even though some consider the 16-member commission it would create to be imperfect.

“This commission is flawed in at least three respects,” Sen. R. Creigh Deeds (D-Bath), the elections committee chairman, said after voting for it. First, he said, the amendment does not contain language specifying the criteria that the commission will use to draw new political boundaries.

Second, it allows lawmakers to sit on the commission; and finally, he said, it dictates that any new map come back to the General Assembly for a final up-or-down vote.

“I would rather have a constitutional amendment that took legislators completely out of the process,” Deeds said.

Eight members of the commission would be legislators — two each from the minority and majority parties of both House and Senate. The other eight would be citizens that the General Assembly would pick from a group selected by a panel of judges.

The committee opted to fix the issue of criteria for drawing the state’s political map by passing enabling legislation to accompany the amendment. It sets out rules for the commission to follow, calling for districts that are similar in population, respect communities of interest, give minorities equal opportunity, don’t favor any political party, and are compact and follow established boundaries as much as possible.

The rules incorporate language from the federal Voting Rights Act, enshrining those protections for minorities in the event that Congress or the courts water down the federal law.

Assuming the bills get through the finance committee, they would go to the full Senate before next Tuesday’s deadline for all legislation to “cross over” — the date by which all bills passed by the Senate go to the House and vice versa.

The House has yet to take up the amendment, and Del. Marcia S. “Cia” Price (D-Newport News) has offered a competing measure that would set up a nonpartisan commission for next year that would not be a part of the state constitution.