Gwynedd council has deferred for a year arts funding cuts which could close the Lloyd George Museum in Llanystumdwy.
Lib Dem AM William Powell said it was a great tourist attraction which had offered a "significant boost" to the local economy.
The Welsh government said it was a matter for Gwynedd council.
On Tuesday, Gwynedd council's cabinet deferred a decision on the museum's future until April 2017.
But council leader Dyfed Edwards said the authority could not continue to run the museum in the long term.
Lib Dem AMs William Powell and Aled Roberts have now called on the Welsh government to make it part of the National Museum of Wales.
They said it would "safeguard the memory of our great Welsh Prime Minister, whose leadership helped save Great Britain from defeat in the Great War".
David Lloyd George, Britain's last Liberal prime minister, took over from Herbert Asquith at the height of the conflict in 1916, serving as head of a coalition government until 1922.
"Wales has every right to be proud of Lloyd George and we should continue to celebrate his life," Mr Powell added.
The Welsh government said the future of the museum was a matter for Gwynedd council, but it was considering a report into local museums across Wales, which were "particularly vulnerable at a time of decreasing finances".
A spokesperson added that Ken Skates, deputy minister for culture, had previously said an additional National Museum in north Wales could be of "great benefit" to the region, and he had asked National Museum officials to consider the idea.
A museum honouring the only Welshman to become prime minister should be taken over by the National Museum of Wales to safeguard it, the Lib Dems have said.