The Quran

وَما كانَ لِمُؤمِنٍ أَن يَقتُلَ مُؤمِنًا إِلّا خَطَأً ۚ وَمَن قَتَلَ مُؤمِنًا خَطَأً فَتَحريرُ رَقَبَةٍ مُؤمِنَةٍ وَدِيَةٌ مُسَلَّمَةٌ إِلىٰ أَهلِهِ إِلّا أَن يَصَّدَّقوا ۚ فَإِن كانَ مِن قَومٍ عَدُوٍّ لَكُم وَهُوَ مُؤمِنٌ فَتَحريرُ رَقَبَةٍ مُؤمِنَةٍ ۖ وَإِن كانَ مِن قَومٍ بَينَكُم وَبَينَهُم ميثاقٌ فَدِيَةٌ مُسَلَّمَةٌ إِلىٰ أَهلِهِ وَتَحريرُ رَقَبَةٍ مُؤمِنَةٍ ۖ فَمَن لَم يَجِد فَصِيامُ شَهرَينِ مُتَتابِعَينِ تَوبَةً مِنَ اللَّهِ ۗ وَكانَ اللَّهُ عَليمًا حَكيمًا

Muhammad Asad

AND IT IS not conceivable that a believer should slay another believer, unless it be by mistake.¹ And upon him who has slain a believer by mistake there is the duty of freeing a believing soul from bondage and paying an indemnity to the victim's relations,² unless they forgo it by way of charity. Now if the slain, while himself a believer, belonged to a people who are at war with you,³ [the penance shall be confined to] the freeing of a believing soul from bondage; whereas, if he belonged to a people to whom you are bound by a covenant, [it shall consist of] an indemnity to be paid to his relations in addition to the freeing of a believing soul from bondage.⁴ And he who does not have the wherewithal shall fast [instead] for two consecutive months.⁵ [This is] the atonement ordained by God: and God is indeed all-knowing, wise.

On the strength of this verse, read in conjunction with verse 93, some of the Mutazilite scholars are of the opinion that a believer who deliberately kills another believer must be considered an unbeliever (Razi). This does not, of course, apply to the execution of a death sentence passed in due process of law.
Lit., "his people" - i.e., the heirs or dependants of the victim. The "freeing of a believing soul from bondage", mentioned three times in this verse, refers in the first instance to persons who have been taken captive in war (see note on 8:67 and also note on 58:3).
Lit., "who are hostile to you" - implying that they are in an actual state of war.
This relates to cases where the victim is a non-Muslim belonging to a people with whom the Muslims have normal, peaceful relations; in such cases the penalty is the same as that imposed for the killing, under similar circumstances, of a fellow-believer.
I.e., in the way prescribed for fasting during the month of Ramadan (see 2:183-187). This alleviation applies to a person who cannot afford to pay the indemnity and/or purchase the freedom of a slave (Razi), or cannot find a slave to be freed, as may be the case in our times (Manar V, 337).