Musk said he had no choice but to reject an emergency request from Ukraine "to activate Starlink all the way to Sevastopol."
Iohannis was speaking a day after Kyiv said Russian drones had detonated on Romanian territory, a claim Bucharest denied.
The US government has so far provided more than $43 billion in weaponry and other military aid to Ukraine.
Reuters' witnesses heard several blasts which sounded like air defense systems being deployed at around 05:50 a.m.
Russian military aircraft were damaged and civilian aviation was disrupted in the drone attacks, said Russian officials.
The Ukrainian military reported shooting down four cruise missiles out of up to eight total airborne targets detected, adding that the rest of the targets were "probably false."
The crash occurred on Friday over the Zhytomyr region, which lies west of Ukraine's capital Kyiv.
Kyiv did not provide details of the Russian regrouping but said the forces continued heavy artillery and mortar shelling and air assaults.
Residents in central Kyiv said they liked having the wrecked Russian hardware on display and that they hoped it would raise the fighting spirit of Ukrainians.
A couple and their 23-day-old baby have been killed in the attack, their son is the lone survivor.