WASHINGTON (CNN) -- President Bush vetoed an expansion of the federally funded, state-run health insurance program for poor children for a second time Wednesday, telling Congress the bill "moves our country's health care system in the wrong direction."

In his veto message, President Bush calls on Congress to extend funding for the current program.

In his veto message, Bush said the bill is almost a duplicate of the proposal he spiked in October.

"Because the Congress has chosen to send me an essentially identical bill that has the same problems as the flawed bill I previously vetoed, I must veto this legislation, too," he said in a statement released by the White House.

The bill would have expanded the State Children's Health Insurance Program by nearly $35 billion over five years, the same as the measure Bush vetoed October 3. Track recent and historical presidential vetoes »

The president had proposed adding $5 billion to the program and said the version he vetoed would have encouraged families to leave the private insurance market for the federally funded, state-run program.

Democratic leaders said the new version addressed Republican objections by tightening restrictions on illegal immigrants receiving SCHIP benefits, capping the income levels of families that qualify for the program and preventing adults from receiving benefits.

Though the measure had strong bipartisan support, it fell short of the two-thirds majorities needed to override a presidential veto in the House and Senate.

House Minority Leader John Boehner, R-Ohio, said Democrats were more interested in scoring political points with the veto than in reaching a compromise with Republicans.

"We could have resolved the differences in his program in 10 minutes, if the majority had wanted to resolve the differences," Boehner said. "This has become a partisan political game."

The program currently covers about 6 million children whose parents earn too much to qualify for Medicaid -- the federal health insurance program for the poor -- but who can't afford private insurance.

Democrats wanted to extend the program to another 4 million, paying for it with a 61-cent-per-pack increase in the federal tax on cigarettes.

"What a sad day that the president would say that rather than insuring [millions of] children, 'I don't want to raise the cigarette tax,' " said House Speaker Nancy Pelosi.

She called for a January 23 vote on whether to override the veto.

Meanwhile, Bush called on Congress to extend funding for the current program to keep the 6 million now covered on the rolls. E-mail to a friend

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