For the second consecutive Friday, clashes along the Gaza-Israel border were less violent than in previous weeks, although 25 Palestinians were injured by Israeli army fire, the territory's health ministry said.
Hundreds of demonstrators gathered at points along the frontier but most kept a distance from the separation barrier, correspondents said.
In Qatar's operation, a total of $90 million is to be distributed in six monthly instalments of $15 million, according to authorities, primarily to cover salaries of officials working for Hamas, the Islamist movement that rules the Palestinian enclave.
Some exited post offices, where the first instalment was being distributed, to show off hundred-dollar bills before the cameras, after several months of sporadic salary payments in cash-strapped Gaza.
The money was driven into the Palestinian enclave through Israel late Thursday by Qatar's envoy to Gaza, Mohammed al-Emadi, transporting suitcases packed with dollars, according to a Hamas source.
Qatar has also said it would hand out $100 to each of 50,000 poor families, as well as larger sums to Palestinians wounded in clashes along Gaza's border with Israel.
"I came to collect $400, my salary for July," Fadi Abu Safia, a 35-year-old government employee, said at a post office in Gaza City.
Mohamed Abed al-Hadi, 27, said he would be collecting 700 shekels ($190 dollars), "quite a sum considering the conditions we're living in", as compensation for an injury in the border clashes.
The Israeli-authorised money transfer appeared to be part of a deal that would see cash-strapped Hamas end months of often violent protests along the border in exchange for Israel easing its blockade of Gaza.
Senior Palestine Liberation Organisation official Ahmed Majdalani expressed the discontent of the West Bank-based Palestinian Authority over the deal.
Emadi had "smuggled the money" into Gaza in suitcases like a "gangster", the official said.
"The PLO did not agree to the deal facilitating the money to Hamas that way," Majdalani, who is close to Palestinian president Mahmud Abbas, told AFP.
Such a deal harmed Egyptian efforts to reconcile Hamas and the PA and would allow the Islamist movement to consolidate its control over Gaza, Majdalani said.
Hamas has controlled Gaza since ousting forces loyal to the internationally recognised PA in a near civil war in 2007.
'Capitulation to terrorism'
Israeli Defence Minister Avigdor Lieberman criticised the Qatari money transfer to Gaza.
"This is capitulation to terrorism, and in effect Israel is buying short-term calm with money, while severely undermining long-term security," he said, quoted in Yediot Aharonot newspaper on Friday.
In another Israeli-approved deal, Qatar has started buying additional fuel for Gaza's sole power station, allowing planned outages to be reduced to their lowest level in years.
Egypt and the United Nations have been brokering indirect negotiations for a long-term truce with Israel, against which Hamas has fought three wars since 2008.
Deadly clashes have accompanied the major protests along the Gaza border with Israel that began on March 30, generating at times fears of a new war between the Jewish state and the strip's militant rulers.
At least 220 Palestinians have been killed by Israeli fire, the majority shot during protests and clashes, while others have died in tank fire or air strikes.
One Israeli soldier was killed by a Palestinian sniper.
Israel says its actions are necessary to defend the border and stop infiltrations and attacks, which it accuses Hamas of seeking to orchestrate.
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