Last week, as the war of words continued, Russia said it would stop visa-free travel from Turkish citizens from January 2016 while Turkey advised its citizens against non-essential travel to Russia.
Russia laid out its economic sanctions against Turkey on Monday, such as halting fruit and vegetable imports, in the hope of having a negative impact on Ankara's agricultural sectors.
Mr Putin signed a decree at the weekend banning charter flights and the sale of package holidays, AFP news agency reported.
Dmitry Medvedev, the Russian prime minister, called the moves a "first step" as Russia said it would limit Turkish transport firms and tighten controls on construction contracts.
Mr Davutoglu decried the sanctions as he urged Moscow to "reconsider these measures in both our interests", while reiterating once again Ankara's willingness to talk.