On Monday, US media reported that Trump may halt the construction of the wall until October to avoid the government shutdown.
"There are two budget processes. Right now we are going to end FY 17 [fiscal year 2017] this week. We hope to continue to get funding in that," he explained.
Spicer added that Trump's plans to build the border wall have not changed. The president's priorities to improve the country's immigration policies also remain in place, Spicer added.
Earlier in the day, Trump said in a Twitter message that the wall would be built and would help to enhance US border security.