Russia has described the troop buildup as part of war games. Ukrainian Major-General Oleksandr Rozmaznin, told journalists in Kiev that the number of troops near the border had been reduced but that might just reflect a scheduled rotation of conscripts.
German Foreign Minister Frank-Walter Steinmeier said the slight reduction in troop numbers was a small signal that the border situation was becoming less tense.
The United States and European Union have imposed sanctions on Russian officials since a March 16 referendum in which Crimea voted for union with Russia. The West says the vote was a sham as Russian forces had taken control of the region.
Russia has shrugged off the sanctions, though the absorption of Crimea and its 2 million residents creates a new financial burden as Russia struggles with slow growth, rising inflation, a weak currency and unusually high capital flight this year.
Medvedev indicated he hoped Crimea, which he said had "colossal prospects" for tourism income, would become self-sufficient.
A senior local economic official said the impoverished Black Sea peninsula hopes for an economic leap forward with large-scale investments, state subsidies and tax breaks from Moscow.
"We have underdeveloped infrastructure and poor people. Now all this has just come to an end and we will finally start dynamic development," Rustam Temirgaliyev, Crimea's First Deputy Prime Minister, told Reuters.
The Crimean economy generates some $4 billion a year but is highly dependent on energy supplies from Ukraine and suffered widespread blackouts last week, which Temirgaliyev denounced as a plot by Kiev.
Boosting the local economy and tourism faces big obstacles, not least a decision by the European Union this month to impose heavy tariffs on goods from the annexed region.
Of the 6-8 million tourists a year who visited Crimea before Moscow intervened, more than 60 percent were from Ukraine, many who came by train on state-funded holidays for public sector workers, and only one-quarter from Russia.
Finance Minister Anton Siluanov said last week that Russia would spend up to 243 billion roubles ($6.82 billion) in Crimea this year, to be financed from the budget reserve.
The ultimate cost of its action in Crimea is likely to be far higher: analysts in a Reuters poll last week slashed their forecasts for Russian economic growth.
Crimea, home to Russia's Black Sea Fleet, has an estimated 55-billion-rouble budget deficit, and has relied on Ukraine for 85 percent of its electricity, 90 percent of its drinking water and much of its food.
It biggest industry is tourism as one of the former Soviet Union's few warm seaside resorts but making it an attractive destination for Russians will be more difficult, since most travel by air and have a wider choice of holiday destinations.
Crimea would have to compete with Bulgaria, Turkey, Greece and Egypt, as well as Russia's own brand new $50 billion Black Sea Olympic resort in Sochi.
A young woman in Simferopol who gave her name only as Yulia welcomed Medvedev's visit: "It's always good when top figures pay us visits because they usually bring money and this is what we need."