He refused to address the claims from the other two women, saying judicial proceedings were under way to determine if he was the father of their children, who are aged six and one.
"You will see this president as a father who is prepared to share his love and care," Lugo said.
"Your current personal situation has made you lose all credibility. I beg you to resign"
Alfredo Jaeggli, senator
The Paraguayan leader, elected in April last year, also insisted he would not resign over the scandal despite a call from a senator aligned to his own party.
"Your current personal situation has made you lose all credibility," Alfredo Jaeggli said in a letter submitted to the presidency and congress.
"I beg you to resign."
In the latest case, a 39-year-old day-care center director, Damiana Amarilla, said this week Lugo was the father of her 16-month-old son.
She also alleged he had fathered at least six children in total with various women.
Another woman, an impoverished 25-year-old soap seller named Benigna Leguizamon, is requesting a DNA test to verify her claim that Lugo fathered her six-year-old son.
Lugo resigned as bishop of Paraguay's central San Pedro province in 2004 after administering there for 10 years.
He announced two years later that he was renouncing the status of bishop to run for president.
He won the presidency last April as head of a left-leaning coalition that ended more than 60 years of one-party rule in the poor South American country.
But the Catholic church initially rejected his application for layman's status, changing its mind and relieving him of his vows of chastity only after he won elections last year.