The California law prevents broadband providers from slowing down or blocking websites, as well as charging higher fees for faster speeds.
As State Senator Weiner said in a statement, within minutes of the signing, Attorney General Jeff Sessions "came out of his cave and sued California to strike down the law", but Weiner said he is confident that California will be able to fend off the federal challenge.
California and the Trump administration are feuding over the state's new internet neutrality law that aims to ensure a level playing field on the internet.
Net neutrality has become a rallying cry for liberal activists and younger Americans, who complain of corporate priorities they say are at odds with what they want to see in internet governance.
In response, the California attorney general and 21 other state attorneys general filed a lawsuit in January in the D.C. Circuit Court of Appeals seeking to invalidate the FCC rollback.
FCC Chairman Ajit Pai, who led the effort to reverse net neutrality, said in a statement that "not only is California's internet regulation law illegal, it also hurts consumers". The suit was filed on Sunday with the United States District Court for the Eastern District of California.
A number of other U.S. states would also like to implement their own rules to protect net neutrality, although the FCC's decision clearly forbids such moves.
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The law also marks the latest challenge between Brown's administration and President Donald Trump's Republicans, who have already clashed over environmental and immigration regulations.
Democratic state Sen. Hannah-Beth Jackson, one of the sponsors of the bill, said the law was necessary because only 75 percent of California-based companies have a woman on their boards, "despite numerous independent studies that show companies with women on their board are more profitable and productive".
The lawsuit argues that the Californian legislation is "unlawful and anti-consumer", as it imposes restrictions on telecommunications companies. An identical bill was introduced in NY.
California Attorney General Xavier Becerra said on Sunday the Trump Administration was ignoring "millions of Americans who voiced strong support for net neutrality rules" while California, which is "home to countless start-ups, tech giants and almost 40 million consumers - will not allow a handful of power brokers to dictate sources for information or the speed at which websites load".
Consequently, numerous other 25-odd states mulling over passing their own net-neutrality laws are undoubtedly going to keep tabs on the outcome of this trial, making this crucial to the fate of net-neutrality in the U.S.
"I am hopeful that our incoming Legislature and governor will agree that the right to choose isn't just a slogan, but rather a commitment to improving true access to abortion for students across California", she said in a statement.