Straw, beginning a two-day visit to the Middle East on Tuesday by meeting Israeli Foreign Minister Silvan Shalom, condemned a Palestinian rocket attack in the Gaza Strip that killed two people and wounded six others.
He said such violence "illustrates the wanton, random terror which Hamas and other similar organisations are ready to practice" to undermine peace efforts and the government of Palestinian President Mahmoud Abbas.
The attack came after Israeli forces killed a local leader of the resistance movement Islamic Jihad in the West Bank.
"Our policy is clear," Straw said at the start of the meeting. "We will have no dealings with the leadership of Hamas or other such organisations unless and until they wholly renounce violence and they renounce their charter calling for the destruction of the state of Israel."
"We will not drop our moral, religious and national constants just to have an audience with Straw and the likes of Straw"
Hamas spokesman in the West
A Hamas spokesman said Straw had no right to make demands of the resistance group.
Hasan Yousuf, Hamas spokesman in the West Bank, told Aljazeera.net: "We will not drop our moral, religious and national constants just to have an audience with Straw and the likes of Straw.
"Resistance to evil is not only a human right, it is a noble moral and national duty," he said.
Earlier, Straw said in a radio interview that British diplomats recently met two mayors in the West Bank and Gaza who were elected to represent Hamas.
Hamas did well in local elections in the West Bank and Gaza Strip recently, leading to predictions of a strong showing in parliamentary elections, where it is to field candidates for the first time.
The election, originally set for 17 July, has been postponed indefinitely. Shalom said Hamas is trying to scuttle tentative Israeli-Palestinian peace moves.
Hamas did well in local elections
in the West Bank and Gaza Strip
"Hamas is trying very hard to undermine our efforts to move toward peace with the Palestinian Authority," he said. "Hamas is trying to undermine Abu Mazin's regime as well," he said, referring to Abbas by his nickname.
During his stay, Straw will have further talks with Israeli and Palestinian leaders, ahead of Israel's planned August pullout from the occupied Gaza Strip and part of the West Bank.
Straw offered his support. "We see it as a key step towards what we all want to see, which is those two states of Palestine and Israel being able to live side by side in peace and security," he said.
On Wednesday he is to meet Abbas, Palestinian Prime Minister Ahmad Quraya and Foreign Minister Nassir al-Kidwa in the West Bank city of Ram Allah, then see Israeli Prime Minister Ariel Sharon in Jerusalem.