Solagh said: "Iraqi-Syrian borders have now become more disciplined... Syrian forces are now contributing to preventing terrorists from crossing into Iraq."
The Syrian authorities have recently put up 4m-high sand berms on some parts of the common border, Solagh said.
He said the Iraqi authorities have not arrested any alleged fighters near the Syrian border for the past two weeks.
"This is something positive. We hope calm will continue," he said.
Solagh said attacks in Iraq have dropped by 70% recently.
He also said the capability of the Iraqi army and interior ministry forces will be considerably boosted within about six months and will be capable of taking full control of security by the end of 2006.
"American troops will not withdraw from Iraq before the Iraqi forces are fully capable of controlling the situation," Solagh said.
The Iraqi minister also said he issued orders on Sunday to release 22 Kuwaitis and eight Saudis who were arrested a few days ago after entering Iraq for hunting.
Concerning a dispute with Kuwait over a metal barrier along their shared border, Solagh said a joint ministerial committee is studying the issue to find a solution for a number of Iraqis living along the border.
"We fully respect the UN Security Council resolutions," on the demarcation of the Iraqi-Kuwaiti borders, the minister said.
A 1993 UN Security Council resolution marked the land and sea border between Iraq and Kuwait, granting Kuwait part of the southern port of Umm Qasr. The resolution was accepted by Iraq in 1994.
Kuwait controls part of the
southern Umm Qasr port
Hundreds of Iraqis earlier this year tore down parts of a metal barrier put up by the Kuwaiti authorities, which locals said was just over the border inside Iraqi territory.
Kuwait insisted the barrier was inside its territory, aimed at stopping illegal infiltrations and smuggling.
Kuwait began the construction of the barrier several months ago to replace a sand mound that had been in place for a decade.