Sorry, OzSpen for the delay:
10“When you approach a city to fight against it, you shall offer it terms of peace. 11“If it agrees to make peace with you and opens to you, then all the people who are found in it shall become your forced labor and shall serve you. 12“However, if it does not make peace with you, but makes war against you, then you shall besiege it. 13“When the LORD your God gives it into your hand, you shall strike all the men in it with the edge of the sword. 14“Only the women and the children and the animals and all that is in the city, all its spoil, you shall take as booty for yourself; and you shall use the spoil of your enemies which the LORD your God has given you. 15“Thus you shall do to all the cities that are very far from you, which are not of the cities of these nations nearby. 16“Only in the cities of these peoples that the LORD your God is giving you as an inheritance, you shall not leave alive anything that breathes. 17“But you shall utterly destroy them, the Hittite and the Amorite, the Canaanite and the Perizzite, the Hivite and the Jebusite, as the LORD your God has commanded you, 18so that they may not teach you to do according to all their detestable things which they have done for their gods, so that you would sin against the LORD your God." (Deuteronomy 20:10-18 NASB)
You can see the Muslims have their own particular spin on it.
The whole of Deut 20 deals with Israel's war against its enemies.
Notice vv 10-12 of the passage you quoted:
10“When you approach a city to fight against it, you shall offer it terms of peace. 11“If it agrees to make peace with you and opens to you, then all the people who are found in it shall become your forced labor and shall serve you. 12“However, if it does not make peace with you, but makes war against you, then you shall besiege it.
So the starting point is to offer peace. For the Muslim, the Quran tells them to kill unbelievers in Islam. I don't find the approach to be identical of the OT and the Quran.
Oz