Maduro made the comments Monday during a meeting of his council of ministers in the government palace.
"I want 20,000 Syrians, Syrian families, to come to Venezuela and share this land in peace," The Associated Press quoted Maduro as saying.
The socialist president reiterated his support for Syrian President Bashar Assad, who has had close ties to Venezuela in recent years.
Since civil war broke out in 2011, more than 4 million Syrians have fled the country, more than any other refugee crisis in almost 25 years, according to the United Nations.