Friedman's push picked up steam in May after the Trump administration moved the embassy from Tel Aviv to Jerusalem over the vehement objections of the Palestinians, who claim the eastern part of the holy city as the capital of an eventual state.
Pompeo said the "single diplomatic mission" will assist Palestinians in the West Bank, Gaza and Jerusalem with consular support "through a new Palestinian Affairs Unit inside U.S. Embassy Jerusalem".
However, the announcement follows the United States closure of the Palestinian Authority's mission in Washington DC in September.
Pompeo said in the statement that the USA has "taken no position on final status issues, including boundaries or borders".
Relations between the sides have been tense since President Donald Trump made a decision to move the USA embassy from Tel Aviv to Jerusalem, recognising the city as Israel's capital despite its status being disputed by the worldwide community and Palestinian claims that East Jerusalem should be the capital of their own state as part of a negotiated two-state solution.
Erekat added: "To end the existence of the US Consulate therefore has nothing to do with "efficiency" and a lot to do with pleasing an ideological US team [and] reward [ing] Israeli violations and crimes".
"The Trump administration is making clear that it is working together with the Israeli government to impose Greater Israel rather than the two-state solution on the 1967 border".
The consulate downgrade is just the latest in a series of decisions by Trump that the Palestinians say shows bias against them.More news: Again - Threatens to Send Military to US-Mexico Border
The embassy was officially transferred on May 14, sparking violent protests in Gaza in which more than 60 Palestinian protesters were killed by Israeli fire.
Arab ambassadors are also deeply concerned at the idea of moving Australia's embassy in Israel to Jerusalem. However, since 1995 it has been US law to recognize Jerusalem as Israel's capital and move the US Embassy to Jerusalem, mandates that the Trump Administration has boldly implemented.
But the Palestinian leadership rejected Pompeo's remarks.
Ofer Zalzberg of the International Crisis Group think-tank said Thursday's announcement meant that the United States would be the only major power without a separate, independent representative office for the Palestinians.
Member of the Knesset Michael Oren, who serves as deputy minister of diplomacy in the Prime Minister's Office, said Israel is "deeply grateful".
It should be further recognised that the PM's reviews of both the Iran and Jerusalem issues will also be well received by our most important strategic ally in Washington - a critical national interest consideration at a time when Australian security and economic concerns vis-a-vis North Korea and China loom larger than ever.
"Every state has the right to determine where within its sovereign territory its capital should be located", he said.
Trump has been angered by the Abbas boycott and has cut hundreds of millions of dollars in aid in a bid to force them back to the negotiating table.