Kvesic reported for duty on Sunday night while Botha arrives on Monday after Exeter flanker Tom Johnson (knee) and Northampton forward Calum Clark (shoulder) were injured during this weekend's Heineken Cup action.
Johnson and Clark will remain at their clubs for treatment. The Rugby Football Union also announced that Harlequins wing Ugo Monye would join training while players involved in European games over the past few days are assessed.
Johnson was carried off just 13 minutes into Exeter's Pool Five game against Leinster on Saturday night, and he looks unlikely to be fit for the opening RBS 6 Nations exchanges against Scotland and Ireland early next month. Speaking immediately after the match, Exeter head coach Rob Baxter said: "Tom has done something to his knee and his ankle, but until we get it scanned we will not know how serious it is."
Clark was named earlier this month in the England elite player squad. He served a 32-week ban last year that ruled him out of action between March and November. He was suspended after being cited for "hyper-extending" Leicester hooker Rob Hawkins' arm during the LV= Cup final.
Germany-born Kvesic, 20, has been in outstanding form for Worcester this term and he was considered unlucky by many pundits to miss out on England boss Stuart Lancaster's squad ahead of the Six Nations.
Kvesic told Worcester's official website: "I have been fortunate to have a run of games at Warriors, and now I am delighted to get the call from England. It would be fantastic to get the opportunity to feature in the Six Nations, but my priority now is meeting up with the team, keeping my head down and working hard to try and make that a reality."
There were several call-ups on Sunday night to the England Saxons squad ahead of their appointment with Irish Wolfhounds in Galway next Friday night.
London Irish back-row forward Jamie Gibson takes Kvesic's place, while Harlequins hooker Rob Buchanan, Gloucester prop Nick Wood, Saracens lock George Kruis, Leicester prop Kieran Brookes are respective replacements for injured quartet David Paice, Nathan Catt, Tom Palmer and Henry Thomas.
And Leicester number eight Jordan Crane, who helped Tigers beat Toulouse in the Heineken Cup on Sunday, is in for highly-rated Wasps prospect Billy Vunipola, who is training with the senior England squad.
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