"The government is serious about the passage of the law as soon as possible," Social Affairs and Labour Minister Faisal al-Haji told state news agency KUNA, adding the issue was discussed during Sunday's cabinet session.
"Women practice their political rights in most countries in the world, including Islamic Gulf states, even becoming ministers," said Haji, who is also acting information minister.
"Democracy will be complete only with the joining of its two wings, men and women," he said.
"Social norms should not become an obstacle barring women from attaining full political rights."
In 1999, Kuwait's Emir Shaikh Jabar al-Ahmad al-Sabah issued a decree granting women the vote but it was defeated in the 50-man parliament by an alliance of MPs.
Last May, the government referred another bill to the house but the assembly has not set a date for a debate.
Sabah's decree was defeated by
a group of MPs
Kuwaiti women serve as diplomats, run businesses, lead the humanitarian and education sectors and help steer oil and banking industries.
But they have had to watch their sisters make modest progress in other Gulf states, such as Bahrain and Qatar where they can vote and stand for election, without gaining the same rights.
Kuwaiti officials have said pressing ahead with reforms is a priority as the oil-rich Gulf state promotes itself as a modern, investor-friendly nation.
On Wednesday, 10 liberal, independent and Shia MPs filed a motion to refer the election law to the Constitutional Court to rule on Article 1, which limits voting rights and candidacy to males above 21 years of age, Arab Times reported.
The MPs said the law violated Kuwait's constitution which stipulates gender equality.
Women have edged closer to political participation after some Islamist MPs said last year they would support the female vote, but not moves to allow women candidates in parliamentary polls.
Haji said the government had asked parliament to debate the election draft as soon as possible, urging the house to pass it.