"We have an administration more focused on securing Ukraine's border than our own, and a House that couldn't pass a border package right now anyway!" Kennedy wrote on X, formerly known as Twitter.
He further stated that illegal border crossings in the US set a new record in September, making it the third record-setting year in a row.
Border patrol agents also arrested 18 people on the FBI terror watchlist in September, the politician added.
Kennedy has promised, if elected president, to secure the US border and eliminate the cartels' drug trafficking economy.
Last week, the Biden administration requested $106 billion in extra funding. The supplemental package includes $61.4 billion for Ukraine, half of which is to provide Kiev with weapons and replenish US military stocks. It also seeks $14.3 billion in assistance for Israel. There is also a request of $6.4 billion to fund operations on the US southern border.
The US House of Representatives is limited in its ability to pass legislation after ousting Congressman Kevin McCarthy as speaker and remaining leaderless. The US Congress must also pass government funding measures before November 17 or face a shutdown.