He made the appeal when receiving members of the Forum of Rectors of Islam Universities at the state palace here on Tuesday.
"I have visited Pakistan. I saw some of our children studying there including in Islamic boarding schools. Many of them are good but there are also hardline schools," he said.
President Yudhoyono also said when an upheaval happened in Yemen several years ago there were reports that several Indonesian students from hardline schools there took part in the fight.
"I am sad to hear that. They are supposed to learn Islam there and so they must not take part in the political affairs in that country. With that stance we could get knowledge and would not bring bad things from that country," he said.
To prevent them from happening again he said he had asked offices concerned to be more selective in giving visas to those wishing to study abroad.
He said very extreme schools abroad have the potential to "produce new extremism in Indonesia."
The behavior, he said, would only make their parents, who hope that their children would return to be great clerics or Islamic intellectuals, sad.
"Their parents hope by studying abroad their children would become Islamic intellectuals, their knowledge increase. But suddenly they bring extremism, show extreme behavior. That makes them sad. Moreover if they become suicide bombers," he said.
In view of that he urged leaders of Islam high-learning institutes in the country to improve their quality and take an active part in the fight against radicalism.
"Save them, by improving the quality of the institutes you are leading so that they would not go abroad to study," he said.
President Yudhoyono underlined the importance of fighting in the Islamic way and prevent evils referring to the act of suicide bombing.
"Save our children and prevent them from doing that, killing themselves and their brothers," he said.
President Yudhoyono was flanked by education minister Mohammad Nuh, religious affairs minister Suryadharma Ali, cabinet secretary Dipo Alam and minister/state secretary Sudi Silalahi in the meeting.
Reporting by GNC Aryani