Rubio's warning follows separate news that Ukraine and the US took the first step towards striking a minerals deal, after an initial agreement was derailed when a February meeting between Trump and Zelensky erupted into a public shouting match.
On Thursday, the two countries signed a memorandum of intent stating that they intend to establish an investment fund for Ukraine's reconstruction as part of an economic partnership agreement.
The aim is to finalise the deal by 26 April, the memo published by the Ukrainian government says.
The details of any deal remain unclear. Previous leaks have suggested the agreement has been extended beyond minerals to control of Ukraine's energy infrastructure, as well as its oil and gas.
Ukrainian negotiators have tried to resist Trump's demands that a joint investment fund would pay back the US for previous military aid, but have seemingly accepted his claim that it would help the country recover after the war ends.
The memo said the "American people desire to invest alongside the Ukrainian people in a free, sovereign and secure Ukraine".
Zelensky had been hoping to use the deal to secure a US security guarantee in the event of a ceasefire deal, telling European leaders last month that "a ceasefire without security guarantees is dangerous for Ukraine".
The US has so far resisted providing Kyiv with security guarantees.
The White House argues the mere presence of US businesses would put off Russia from further aggression, but that did not exactly work when they invaded in 2022.