WASHINGTON — Senior House Democrats, including Bay State Representatives Edward Markey and Barney Frank, urged Speaker John Boehner and other Republicans on Wednesday to relaunch bipartisan negotiations to avoid automatic budget cuts that are scheduled to go into effect at the start of the year.

In a letter to Boehner and other members of the GOP leadership, ranking Democrats on 21 House committees issued their call for a “balanced deficit reduction plan” to avoid going over a “fiscal cliff” — and called for meetings before Congress adjourns for a nearly month-long recess at the end of next week.

“We all agree that a sequester starting in January, 2013 is not in the country’s best interest and is not the best way to assure responsible deficit reduction. The American people want us to work together to avoid unnecessary economic uncertainty at this crucial time in our recovery. Failure to reach an agreement would have devastating consequences for our economy, small business, and the middle class.”

While the letter did not specify what would constitute a “balanced approach,” the oft-used phrase by Democrats has been code for creating a revenue stream to minimize the spending cuts advocated by Republicans.

The letter was sent out to reporters as the Senate, presided over by Vice President Joe Biden, continued debate over extending the Bush tax cuts, which would automatically expire at the end of the year. Republicans want the tax cuts extended, while Democrats sought to extend the cuts only for people earning less than $250,000 a year — providing a long-sought revenue stream that Democrats hope could help set aside the sequester.

Under the sequestration plan already approved by Congress, $1.2 trillion in cuts would have to be made to federal budgets over the next 10 years to reduce federal deficits. The first round of cuts, totalling $110 billion, would be rolled out at the start of next year. About half the cuts would come from the Pentagon, with the other half exacted across other federal programs.

Republicans have been trying to undo the defense cuts. Last week, they passed a $606 billion defense spending bill that would throw out the sequester funding levels for defense.

They leveled blame on President Obama and other Democrats.

“The sequester is happening because the president didn’t lead,” Boehner said. “He wanted an increase in the debt ceiling, without spending cuts and reforms that are truly needed to reduce our deficit and our debt. He wanted an increase in the debt ceiling so that he wouldn’t have to deal with it twice before his election. So rather than agree to tax and entitlement reforms that everyone knows are needed, the president and Senate Democrats gave us the sequester, promising that the cuts would never actually happen.

“Now some of those same Democrats are threatening to drive us off the ‘fiscal cliff’ and tank our economy all in their quest for higher taxes. The House has already passed legislation to replace the looming defense cuts with common sense reforms. We’ve done our job.”

Democrats, however, accused Republicans of turning their backs on last year’s budget agreement. A bipartisan supercommittee comprised of members from both chambers of Congress was convened last fall to avoid sequestration, but failed to bridge the substantial divides over spending and taxes.

Back then, Democrats pointed out this week, Boehner said he would allow the automatic cuts to proceed if the supercommittee failed to reach an agreement.

“I would feel bound by it,” Boehner said. “It was part of the agreement. And so either we succeed or we are in the sequester. The sequester is ugly. Why? Because we don’t want anybody to go there. That’s why we have to succeed.”