"That wall has started, we have 1.6 billion (dollars)," Trump said at a campaign rally in Washington, Michigan.
"We come up again on September 28th and if we don't get border security we will have no choice, we will close down the country because we need border security."
Trump made a similar threat in March to push for changes in immigration law that he says would prevent criminals from entering the country. The government briefly shut down in January over immigration.
A $1.3 trillion spending bill, which Trump signed last month, will keep the government funded through the end of September. A government shutdown ahead of the November mid-elections is unlikely to be supported by his fellow Republicans who are keen to keep control of the U.S. Congress.