The Ukrainian army has set up checkpoints around Luhansk and other eastern cities. BBCGermany's Foreign Minister Frank-Walter Steinmeier is due in Kiev amid fresh attempts to find a diplomatic solution to the Ukraine crisis.
On Monday, pro-Russia activists in the east declared a separate state which wanted to join Russia after holding votes on self-rule on Sunday.
Earlier, a separatist leader called on Russia to "absorb" the eastern Ukrainian region of Donetsk.
Kiev, the US and EU say the referendums in Donetsk and Luhansk were illegal.
Moscow annexed Ukraine's southern autonomous republic of Crimea in March following a controversial referendum, and Kiev fears a similar outcome in Donetsk, Luhansk and parts of southern Ukraine.
Russia has called for the results of Sunday's vote to be "implemented".
Meanwhile, armed separatists remain in control of many official buildings across eastern Ukraine.
Mr Steinmeier, who attended a meeting of EU foreign ministers in Brussels on Monday, reiterated that he considers the referendums illegal, adding: "We cannot, and must not, take it seriously."
His spokesman, Martin Schaefer, said Tuesday's trip was to support a national "round table" under the auspices of the Organisation for Security and Co-operation (OSCE).
The OSCE later issued a statement saying Russian President Vladimir Putin was "supportive" of its roadmap to defuse the crisis in Ukraine.
Mr Steinmeier has engaged in months of diplomacy over the crisis while German Chancellor Angela Merkel has held repeated phone calls with President Putin.
The EU foreign ministers added 13 people and two businesses to its sanctions list for "undermining or threatening" Ukraine's sovereignty.
Those singled out include President Putin's first deputy chief of staff, Vyacheslav Volodin; the self-declared mayor of Sloviansk, Vyacheslav Ponomaryov; and two Crimean companies.
More than 60 individuals now face EU travel bans and asset freezes.
Germany, France and the UK also suggested that Russia would be further punished if it undermined Ukraine's planned presidential elections on 25 May.
A joint statement said the EU would "pay particular attention to all parties' attitude and behaviour towards the holding of free and fair presidential elections when deciding about possible future measures".
Separatists in Donetsk and Luhansk say 89% and 96% respectively voted in favour of "self-rule" in the referendums.
Pro-Russia activists in Luhansk declared independence after the referendum there.
Self-declared Donetsk People's Republic leader Denis Pushilin urged Moscow to listen to the "will of the people".
He said he was not calling for Russian military intervention, but that "peacekeepers" may be needed. Moscow has not responded to his comments.
Nato believes some 40,000 Russian troops are deployed near Ukraine's border, although Moscow says they have been pulled back.