Democratic presidential candidate Bernie Sanders speaks at a town hall event in Muscatine, Iowa, on Dec. 29, 2015. (REUTERS/Mark Kauzlarich)

DES MOINES, Iowa -- The two leading Democratic presidential candidates renewed their sparring Thursday over how to pay for a promise they’ve both made to guarantee workers paid leave after a family has a child.

On the eve of a planned press conference on the subject by Bernie Sanders, the campaign of Hillary Clinton issued a statement from a policy adviser saying “this is not a new fight” for the Democratic front-runner and attacking Sanders for wanting to raises taxes on workers to pay for the benefit.

“Hillary believes we can do this without asking working people to pay for it,” said Clinton senior policy adviser Ann O’Leary. “Her view is that we can ask the wealthy to pay their fair share in taxes and that will cover paid leave. We look forward to what Senator Sanders has to say.”

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Sanders decided not to wait for his press conference, scheduled for Friday morning in Cedar Rapids, Iowa, to say something.

A younger member of the audience at a rally for Sen. Bernie Sanders (I-Vt.) chimes in as Sanders discusses paid family leave in this video released by his presidential campaign. (Bernie 2016)

He made it known later Thursday afternoon that he is “disappointed” in Clinton for her refusal to support legislation pending in Congress to accomplish the goal that they both back.

The bill, introduced by Clinton’s successor in the U.S. Senate, Kristen Gillibrand (D-N.Y.), would provide three months of paid family leave for new parents and people with serious illnesses, and it would be paid for by an increase in the payroll tax that Sanders says would amount to $1.61 a week.

“Bernie thinks that’s a good investment,” said Sanders spokesman Michael Briggs. “What Secretary Clinton might not appreciate is that we’re talking about the same kind of modest investment our country has made before in two critically important programs for working families: Social Security and Medicare.”

Briggs also questioned whether Clinton would veto Gillibrand’s bill if it reached her desk during a Clinton presidency. He noted the Senate version of the bill has 19 co-sponsors and a similar House measure has 119 co-sponsors, including some of the most liberal members of Congress.

The back-and-forth over this issue is not new. In recent weeks, Clinton has made the case that she is the only Democrat running who has promised not to raise taxes on the middle class. That was a point she raised as recently as Wednesday night, when all three Democratic candidates for president appeared in Las Vegas for a dinner sponsored by the Nevada Democratic Party.

Regarding Sanders's tax plans, Clinton points both to Sanders’s embrace of the family leave legislation and a proposal he has pushed to move to a single-payer health-care system.

Under the latter plan, taxes would increase, but Sanders says the typical family would save thousands of dollars a year because they would not pay premiums or co-pays.