This paper is aimed at setting observational limits to the number of cosmic strings ( Nambu-Goto , Abelian-Higgs , semilocal ) and other topological defects ( textures ) . Radio maps of CMB anisotropy , provided by the space mission Planck for various frequencies , were filtered and then processed by the method of convolution with modified Haar functions ( MHF ) to search for cosmic string candidates . This method was designed to search for solitary strings , without additional assumptions about the presence of networks of such objects . The sensitivity of the MHF method is \delta T \approx 10 \mu K in a background of \delta T \approx 100 \mu K . The comparison of these with previously known results on search string network shows that strings can only be semilocal in an amount of 1 \div 5 , with the upper restriction on individual strings tension ( linear density ) of G \mu / c ^ { 2 } \leq 7.36 \cdot 10 ^ { -7 } . The texture model is also legal . There are no strings with G \mu / c ^ { 2 } > 7.36 \cdot 10 ^ { -7 } . However , comparison with the data for the search of non-Gaussian signals shows that the presence of several ( up to 3 ) of Nambu-Goto strings is also possible . For G \mu / c ^ { 2 } \leq 4.83 \cdot 10 ^ { -7 } the MHF method is ineffective because of unverifiable spurious string candidates . Thus the existence of strings with tensions G \mu / c ^ { 2 } \leq 4.83 \cdot 10 ^ { -7 } is not prohibited but it is beyond the Planck data possibilities . The same string candidates have been found in the WMAP 9-yr data . Independence of Planck and WMAP data sets serves as an additional argument to consider those string candidates as very promising . However the final proof should be given by optical deep surveys .