WASHINGTON — More families with higher incomes could claim the popular child tax credit under a bill that won approval Friday in the House. But in a dispute that divides Republicans and Democrats, millions of the poorest low-income families would still lose the credit in 2018, when enhancements championed by President Barack Obama are set to expire.

The bill would gradually boost the amount of the $1,000-per-child tax credit by tying it to inflation, so it would go up as consumer prices rise. It also aims to make a dent in illegal immigration by prohibiting people without Social Security numbers from claiming a portion of the credit reserved for low-income families.

With nearly all Republicans voting in favor and most Democrats opposed, the bill cleared the House by a vote of 237-173. The White House threatened to veto the bill, though the Democratic-controlled Senate is unlikely to pass it. About 37 million taxpayers claimed the credit in 2012, reducing their tax bills by nearly $57 billion.

House Republicans say the bill would strengthen the tax credit by increasing it as inflation rises, and by making it available to even more middle-income families. “It is time we make some simple improvements to the child tax credit, so it keeps up with the cost of raising children,” said Rep. Dave Camp R-Mich., chairman of the tax-writing House Ways and Means Committee.

The White House said the bill favors high-income taxpayers over the poor, while adding $90 billion to the budget deficit over the next decade.

Five million of the poorest low-income families would lose the credit in 2018, the White House said.