A completed tie-up would step up pressure on market leader AC Nielsen in an industry which has become increasingly important as companies hunt for more information on their clients and services.
TNS, whose shareholders will vote on a nil-premium merger with GfK on July 18 said advertising and marketing group WPP was just trying to delay the deal.
The German company's investors vote on July 21.
WPP Chief Executive Martin Sorrell shrugged off TNS's rejection, telling reporters on Thursday: "What we are doing is putting this (improved proposal) to the market" when asked if he would put his offer direct to TNS investors.
TNS said: "WPP's successive approaches and considerable press commentary and innuendo collectively represent an attempt by WPP purely to frustrate the merger".
TNS shares were up 2.4 percent at 230.5 pence, while WPP stock had recovered from a five-year low at 448.75 pence in early trading to be up 0.4 percent at 462.25 pence.
"Our clients need more information, they need it faster and they need it from all corners of the world and delivered in an efficient way," GfK Finance Director, Christian Weller, said on June 3 when it agreed to merge with TNS.
"The timing is right for this kind of deal. Our industry is very dynamic. We want to continue to stay ahead of the market and the changes brought about by globalization, digital information and more diverse consumer behavior," Weller said.
But analysts have said from the start that WPP, which would merge TNS with its Kantar business, could disrupt the TNS-GfK deal.
ABN Amro has said it thought WPP could offer up to 285 pence per share, while UBS said it could offer around 300 pence.
WPP, which includes the JWT and Ogilvy & Mather advertising agencies, said its new proposal for TNS was 173 pence in cash and 0.1889 new WPP share for each TNS share.
WPP forecast 52 million pounds of annual synergies by 2011 from a takeover of TNS, at a lower cost in the preceding two years.
It said the cash consideration of a successful offer would be funded by a new debt facility.
Numis Securities analysts said: "Given the general level of economic and stock market uncertainty and high cash component in the bid (67 percent cash), it may be enough to persuade TNS shareholders in this environment."
WPP, which has a July 9 deadline from Britain's Takeover Panel to make an offer for TNS, said it would only make an offer if it got the unanimous recommendation of TNS's board.
