The Ministry of Social Affairs in Gaza announced the beginning of payments from Qatar to about 100,000 needy families in the Gaza Strip.
The peace talks, initially slated for two days, are continuing despite Taliban representatives staging a brief walkout on Friday over differences with US special peace envoy Zalmay Khalilzad.
In an implicit criticism of Israel, the Qatari diplomat said: "There are other parties that are exploiting the humanitarian aid for the internal elections and to score political points."
Approval of the sale comes amid a halt in all weapons sales to Qatar's rival Saudi Arabia imposed by Berlin after the killing of journalist Jamal Khashoggi.
Islamic Jihad, the second largest group in the Gaza Strip after Hamas, voiced support for the Hamas move and called for the continuation of the weekly demonstrations near the border with Israel.
Qatari envoy Mohammed El-Amadi arrived in Jerusalem on Wednesday in an effort to resolve the crisis and sway Israel to release the funds.
His comments came after sniper fire from Gaza lightly wounded an IDF officer along the Gaza border on Tuesday.
Qatari fund transfer talks started again after an IDF soldier was lightly wounded by a terrorist's fire.
Lebanon has one of the world's highest levels of public debt compared to GDP and stagnant growth.
Qatar hopes the aid will ease conditions and restore stability, part of efforts to bolster its international standing amid a diplomatic dispute with Saudi Arabia and other Gulf neighbors.