Memorandums of understanding were adopted between the countries' agriculture ministries, and between the Russian Federal Space Agency and Nicaragua's Telecommunications and Postal Service Institute (Telcor).
Several other departments of the two countries also signed agreements.
Medvedev said after the talks that the main goal in bilateral affairs is to develop trade and economic ties.
"Over recent years, trade has considerably declined," while in Soviet times trade totaled hundreds of millions of dollars, the Russian president said. "Our task is to give an impetus to the development of economic relations, from a new basis."
Medvedev said Russia aims to establish an increasingly strong presence in Latin America.
"I would like our Nicaraguan partners to know that our presence in Latin America, and warm relations with key partners, are not a temporary factor but a deliberate choice."
Medvedev and Ortega said in a joint statement released after the meeting that Russia is interested in participating in the construction of a canal across Nicaragua, linking the Pacific and Atlantic oceans.
"The Russian president accepted the Nicaraguan president's proposal to study the possibilities of participation by Russia's state and private sectors in an enterprise to build an inter-ocean canal in Nicaragua," the statement said.
The proposed canal would be able to accommodate ships larger than those that can pass through the Panama canal, even after its enlargement.
The statement also said Medvedev had accepted an invitation from his Nicaraguan counterpart to pay an official visit to the country.
"Nicaraguan President Daniel Ortega invited Russian President Dmitry Medvedev to pay an official visit to Nicaragua at a time convenient for both parties," the document said. "The invitation was gratefully accepted, and the date of the visit will be coordinated through diplomatic channels."
Russian Deputy Prime Minister Igor Sechin told reporters that Russia plans to develop hydro and geothermal power in Nicaragua.
Nicaragua is a major exporter of coffee, nuts and tobacco to Russia. Russia's main exports to Nicaragua are machinery, equipment and chemicals. Last year, Russian-Nicaraguan bilateral trade reached $6.8 million, and in the first nine months of 2008 hit $5.6 million.