LAGOS (Reuters) - Finance Minister Ngozi Okonjo-Iweala held up a sponge cake representing GDP to an audience of amused officials on Monday, as she sought to rebuff critics who say Nigeria's strong economic growth has failed to lift millions out of poverty.

Likening Nigeria to a household, she urged the country to focus on the government's plan to become one of the world's top 20 economies by 2020, which she said would be crucial to solving its other problems like high unemployment and poverty. It would mean doubling the current growth rate to 13 percent, she said.

"Having this cake does not mean that every problem in your household is solved," she said, holding up a sponge with figurines of a family on it, at a televised conference.

"But you have one wife and three children and ... if you have only this cake you're going to be suffering. You want this cake to grow," she added, swapping the sponge for a much bigger one, prompting a wave of laughter.

Foreign bond and equity investors are taking a growing interest in Africa's second biggest economy, and President Goodluck Jonathan's decision to bring Okonjo-Iweala back to Nigeria from her world bank job in 2011 was well received.

But she has had a mixed reception at home, with some politicians complaining she is too aloof and technocratic.

Just in case anyone in her audience, including ministers and top civil servants, missed the analogy, she added: "Our cake is GDP and it is growing at 6.5 percent. What we want to do is grow the cake as fast as possible while solving the other problems."

Despite a decade of 7 percent economic growth, poverty in Nigeria has worsened, official figures show, leading critics to say its oil dependent economy is merely enriching the few.

Former President Olusegun Obasanjo, who hired Okonjo-Iweala during her first stint as finance minister between 2003-2006, was quoted in the local press last month as saying Nigeria's growth had not lifted the living standards of most Nigerians.

Investors worry that widespread violence and insecurity will only worsen if Nigeria cannot get rid of youth unemployment and poverty, risks that take the shine off its impressive growth.

The minister is trying to win support for moves to increase Nigeria's external debt, tapping into markets that offer much cheaper funding than at home, where monetary policy is tight. ($1 = 159.7000 naira)

(Reporting by Tim Cocks; additional reporting by Chijioke Ohuocha; editing by James Jukwey)