The US Senate has advanced legislation addressing security policy in the Middle East, including new sanctions on Syria and a measure taking aim at boycotts of Israel.

Democrats had blocked the package in the Senate during the 35-day partial government shutdown, saying the chamber should first consider legislation to reopen the government.

But after Friday's agreement to end the shutdown at least until February 15, most of the Senate's Democrats on Monday joined Republicans in favour of taking up the legislation, introduced by Republican Senator Marco Rubio.

The measure is still several steps from becoming law, and may never get there. Even if passed by the Senate, it must also be approved by the House of Representatives, where Democrats hold a majority of seats.

The legislation includes provisions to impose new sanctions on Syria and guarantee security assistance to Israel and Jordan. Those are seen as efforts to reassure Washington's allies worried about shifts in United States's policy since President Donald Trump abruptly announced plans last month for a quick withdrawal of his country's troops from war-torn Syria.

However, the act also includes a controversial measure that combats the Boycott, Divest and Sanctions (BDS) movement, a Palestinian non-violent campaign for human rights.

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It would allow US states and localities to retaliate commercially against companies or individuals supporting BDS.

Opponents consider the BDS provision an impingement of free speech.

"While I do not support the BDS movement, we must defend every American's constitutional right to engage in political activity. It is clear to me that this bill would violate Americans' First Amendment rights," said Senator Bernie Sanders, an independent who caucuses with Democrats and was a "no" vote on Monday.

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Some Republicans accused Democrats of supporting the BDS movement, which aims, among others, to pressure Israel to end its occupation of the Palestinian territories, as well as grant of full citizenship rights to Palestinians in Israel and ensure Palestinian refugees' right of return to the homes that they or their families were expelled from to make way for the formation of the state of Israel in 1948.

In turn, some Democrats accused Republicans of trying to use the BDS measure to divide moderate and liberal Democrats.

Earlier this month, recently sworn-in Representative Rashida Tlaib, a Michigan Democrat and Palestinian-American who supports the BDS movement, condemned the bill on Twitter, saying, "this is the US where boycotting is a right & part of our historical fight for freedom & equality".

The American Civil Liberties Union has also said the anti-BDS measure's inclusion in the wider bill "sends a message to Americans that they will be penalised if they dare to disagree with their government".

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The BDS movement was launched in 2005 by Palestinians seeking to generate international pressure on Israel to respect Palestinian human rights.

Proponents say the effort draws from the anti-apartheid campaign in South Africa in the 1980s and the earlier African American Civil Rights movement of the 1950s and 60s.

Israel sees BDS as a strategic threat and accuses it of anti-Semitism - a claim activists firmly deny, calling it an attempt to discredit them.