Speaking at a campaign rally in Washington, Michigan, on Saturday,Trump said: "That wall has started, we have 1.6 billion (dollars). 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's proposal for the construction of a 2,000-mile wall has been met with strong criticism both at home and abroad.
The construction work began on April 9, with US Customs and Border Protection officials gathering to mark the groundbreaking of the $73-million project at Santa Teresa near New Mexico’s state line with Texas.
In March, Trump made a similar threat to push for changes in immigration law to help prevent criminals from entering the US.
A $1.3 trillion spending bill, which Trump signed last month to keep the government funded through the end of September, authorized only $1.6 billion for fencing, surveillance technology and other measures related to the wall, although the president originally wanted as much as $25 billion for the project.