Almost a quarter of Norway's companies have failed to comply with a controversial law requiring them to increase the proportion of women on their boards to 40%, according to government figures. If they do not promote more women, they could be shut down.

Norway's 487 public limited companies, including 175 firms listed on the Oslo stock exchange, have until the end of the year on Monday to implement a 2003 act that requires firms to boost the number of female directors.

The law, which introduced quotas, has been effective in raising the number of women board members at listed companies from 6% in 2001 to 37%.

Norway now boasts the highest proportion of women on boards in the world. Sweden comes second with 19%; the US has around 15%. In the UK, only 11% of directors were female in 2007.

The Norwegian government hailed the numbers as proof that quotas work.

"This trend would not have happened without regulation," said the gender equality minister, Manuela Ramin-Osmundsen. "Business organisations have tried for 20 years to boost the number of women on boards, but they have been unsuccessful."

When asked whether the government would really shut down companies that do not comply, Ramin-Osmundsen said: "The law is clear - we will enforce the procedures. These have existed for 30 years. They have not come out of nowhere."

Many of the 111 companies yet to comply with the law are in the financial, IT and oil and gas sectors, according to Marit Hoel, head of the Centre for Corporate Diversity. Among affected companies listed on the Oslo bourse, fewer than five have yet to name a single woman. One of them is DNO, a petroleum company that was the first to explore for oil in Iraq's Kurdish region after the war. The quota law was the brainchild of an unlikely feminist: a 52-year-old Conservative trade and industry secretary and former businessman, Ansgar Gabrielsen, who served in a previous cabinet. Gabrielsen's focus was less about gender equality and more about "the fact that diversity is a value in itself, that it creates wealth.

"I could not see why, after 25-30 years of having an equal ratio of women and men in universities and with having so many educated women with experience, there were so few of them on boards," he said.

"From my time in the business world, I saw how board members were picked: they come from the same small circle of people. They go hunting and fishing together. They're buddies."

Outside business, Norwegian women have been successful in reaching top positions. In politics a third of the country's MPs and half of the 18 cabinet ministers are women.

When the bill was announced four years ago, it immediately sparked protest in the business community, with critics arguing that it was too harsh to close a company because its board was one woman short.

"We are still opposed to the principle of the law, as we believe it is the right of company owners to choose," said Sigrun Vågeng at the Confederation of Norwegian Enterprise (NHO).

NHO is no longer campaigning against the law but wants the state to impose fines, rather than closures, as a penalty. It has also set up a training and networking programme that puts female board candidates in touch with company owners.

Since the law was passed in 2003, company owners have led a frantic hunt to find suitable female candidates.

"I am frequently contacted by headhunters," said Mari Thjomoe, 45, a chief financial officer at an insurance company. "I've had five or six invitations to join boards in the last year, and one or two the year before."