JACKSON (AP) — The spokesman for a national anti-tobacco group said Thursday Mississippi and other states should continue trying to increase their cigarette taxes, even as the federal tax on a pack of smokes is growing significantly in just a few weeks.

President Barack Obama signed a law Wednesday that will add 62 cents to the federal cigarette excise tax, setting it at $1.01 a pack starting March 31.

‘‘The states shouldn’t use this as a reason to slow down talks about tax increases,’’ Joel Spivak, spokesman for the Campaign for Tobacco-Free Kids, said in an interview from Washington.

The revenue from the federal cigarette tax increase is supposed to help pay for an expansion of the State Children’s Health Insurance Program, which covers children in families across the nation that earn too much to qualify for Medicaid.

In Mississippi, lawmakers are working on a cigarette tax increase as a way to bolster the state’s lagging budget. The state’s current tax is 18 cents a pack, the third-lowest in the nation.

The state House and Senate have passed separate versions of a tax bill and are moving closer to negotiations for a final amount. But it’s not clear whether the federal action will change the momentum of talks in Mississippi.

The state House has voted to set the tax at $1 a pack.